Events

Operator Theory Seminar

This seminar, organized by Man-Duen Choi, Chandler Davis, George Elliott, and Peter Rosenthal, is devoted, loosely speaking, to the study of all areas of mathematics involving Hilbert space operators. (This has variously been interpreted recently to include matrix theory, index theory of differential operators and other aspects of non-commutative geometry, invariant subspace theory, quantum information theory, C*-algebra classification theory, and string theory.)

Details

Relative determinants and isospectrality on surfaces with cusps

by
Clara Aldana
|
MPIM Bonn
Time: 16:10 (Monday, Mar. 22, 2010)Location: BA6183, Bahen Center, 40 St George StAbstract:
In the talk, I will define the relative determinant of the Laplace operator on a surface with cusps when it is compared to a model operator in the cusp. Then I consider a conformal class of metrics with deformations in a fixed compact set. The meaning of isospectrality for these metrics will be explained. In the next part, I prove compactness of the set of isospectral metrics inside this conformal class. In the proof, I use a splitting formula for the relative determinant of the Laplacian that relates it to the Dirichlet to Neumann operator on a hypersurface. I will also give the proof of the splitting formula.